Finite Group Databasebeta

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C4×C82×C11 #14585031

order2816
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7864320
homologyAbelianization (H1) = G · Schur multiplier (H2) = C42×C8

Aliases

abelianC4×C82×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C42C23×C11
socle, prime radicalC23×C11C2×C42
LCSG ▷ C1
UCSC1 ◁ G

750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 2816

A minimal faithful permutation representation — 3 generators on 31 points:

(1,2,3,4,5,6,7,8)(21,22,23,24,25,26,27,28,29,30,31);(9,10,11,12,13,14,15,16);(17,18,19,20)

Conjugacy classes & character table

2816 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C8×C11×C16, C83×C11, C2×C4×C82×C11, …
maximal normal subgroup ofC4×C8×C11×C16, C83×C11, C2×C4×C82×C11, …
maximal quotient ofC4×C8×C11×C16, C83×C11, C2×C4×C82×C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 826);