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C4×C43×C64 #24927526

order11008
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 43008
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C43×C64
multiplicative(ℤ/13765)ˣ, (ℤ/27530)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C32C22×C43
socle, prime radicalC22×C43C2×C32
LCSG ▷ C1
UCSC1 ◁ G

86 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11008 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C43×C128, C8×C43×C64, C2×C4×C43×C64
maximal normal subgroup ofC4×C43×C128, C8×C43×C64, C2×C4×C43×C64
maximal quotient ofC4×C43×C128, C8×C43×C64, C2×C4×C43×C64
automorphism group ofC5×C2753
outer automorphism group ofC5×C2753

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 497);