Finite Group Databasebeta

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C22×C32×C8×C25 #72186269

order7200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 368640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C32×C8×C25
multiplicative(ℤ/12621)ˣ, (ℤ/16828)ˣ, (ℤ/21636)ˣ, (ℤ/25242)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C5C23×C32×C5
socle, prime radicalC23×C32×C5C4×C5
LCSG ▷ C1
UCSC1 ◁ G

684 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C16×C25, C2×C32×C4×C8×C25, C23×C32×C8×C25, …
maximal normal subgroup ofC22×C32×C16×C25, C2×C32×C4×C8×C25, C23×C32×C8×C25, …
maximal quotient ofC22×C32×C16×C25, C2×C32×C4×C8×C25, C23×C32×C8×C25, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.