Finite Group Databasebeta

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C4×C8×C11×C43 #72193170

order15136
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 53760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C8×C11×C43
multiplicative(ℤ/15397)ˣ, (ℤ/30794)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C22×C11×C43
socle, prime radicalC22×C11×C43C2×C4
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15136 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C11×C16×C43, C82×C11×C43, C2×C4×C8×C11×C43
maximal normal subgroup ofC4×C11×C16×C43, C82×C11×C43, C2×C4×C8×C11×C43
maximal quotient ofC4×C11×C16×C43, C82×C11×C43, C2×C4×C8×C11×C43
automorphism group ofC89×C173
outer automorphism group ofC89×C173

GAP

Past the SmallGroups library coverage — no SmallGroups id.