Finite Group Databasebeta

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C2×C32×C5×C32 #72182661

order2880
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 12288
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC2×C32×C5×C32
multiplicative(ℤ/3007)ˣ, (ℤ/6014)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C22×C32×C5
socle, prime radicalC22×C32×C5C16
LCSG ▷ C1
UCSC1 ◁ G

204 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2880 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C5×C64, C32×C4×C5×C32, C22×C32×C5×C32, …
maximal normal subgroup ofC2×C32×C5×C64, C32×C4×C5×C32, C22×C32×C5×C32, …
maximal quotient ofC2×C32×C5×C64, C32×C4×C5×C32, C22×C32×C5×C32, …
automorphism group ofC31×C97, C2×C31×C97
outer automorphism group ofC31×C97, C2×C31×C97

GAP

Past the SmallGroups library coverage — no SmallGroups id.