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C4×C137 #10587738

order548
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C8×C17 (order 272) · Inn(G) = C1 · Out(G) = C2×C8×C17
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC548
abelianC4×C137

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C137
socle, prime radicalC2×C137C2
LCSG ▷ C1
UCSC1 ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 141
transitive degreeμt(G) = 548

A minimal faithful permutation representation — 1 generator on 141 points:

(1,2,3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141)

Conjugacy classes & character table

548 conjugacy classes. The character table is too large to display.

Relationships

center ofM16×C137, #41×C137, #1320×C137, …
derived subgroup of#14555495, D1096, #14555497, …
Fitting subgroup of#11764040, C4×D137, D548, …
maximal subgroup ofC8×C137, C2×C4×C137, D4×C137, …
maximal normal subgroup ofC8×C137, C2×C4×C137, D4×C137, …
maximal quotient ofC8×C137, C2×C4×C137, Dic3×C137, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(548, 2);