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C41×#442 #14579910

order2624
nilpotency class3
isoclinismisoclinic class of AGL(1,ℤ/8)
automorphism?
homologyAbelianization (H1) = C22×C4×C41 · Schur multiplier (H2) = C23

Aliases

direct productC41×#442

Subgroups

subgroupG/H
center, socleC22×C41C2×D4
commutatorC4C22×C4×C41
Frattini, cosocleC2×C4C23×C41
prime radicalC2×D8×C41C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C42×C41 ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 1312

A minimal faithful permutation representation — 3 generators on 53 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)(42,43,45,44)(46,47,49,51)(48,50,53,52);(47,50)(48,53)(51,52);(42,44,45,43)(47,51)(50,52)

Conjugacy classes & character table

902 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC41×AGL(1,ℤ/16), C2×C41×#442, C41×#2943, …
maximal normal subgroup ofC41×AGL(1,ℤ/16), C2×C41×#442, C41×#2943, …
maximal quotient ofC41×#1580, C41×#1586, C41×#1594, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 123);