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C42×C7×C11 #11927695

order1232
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC42×C7×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C22×C7×C11
socle, prime radicalC22×C7×C11C22
LCSG ▷ C1
UCSC1 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 1232

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4)(9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26);(5,6,7,8)

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C7×C8×C11, C2×C42×C7×C11, C3×C42×C7×C11, …
maximal normal subgroup ofC4×C7×C8×C11, C2×C42×C7×C11, C3×C42×C7×C11, …
maximal quotient ofC4×C7×C8×C11, C2×C42×C7×C11, C3×C42×C7×C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1232, 78);