Finite Group Databasebeta

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C4×C5×C13×C32 #72187237

order8320
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 24576
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C5×C13×C32
multiplicative(ℤ/10405)ˣ, (ℤ/20810)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C16C22×C5×C13
socle, prime radicalC22×C5×C13C2×C16
LCSG ▷ C1
UCSC1 ◁ G

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C13×C64, C5×C8×C13×C32, C2×C4×C5×C13×C32, …
maximal normal subgroup ofC4×C5×C13×C64, C5×C8×C13×C32, C2×C4×C5×C13×C32, …
maximal quotient ofC4×C5×C13×C64, C5×C8×C13×C32, C2×C4×C5×C13×C32, …
automorphism group ofC5×C2081
outer automorphism group ofC5×C2081

GAP

Past the SmallGroups library coverage — no SmallGroups id.