Finite Group Databasebeta

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C22×C4×C5×C112 #72188391

order9680
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 10137600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C11

Aliases

abelianC22×C4×C5×C112
multiplicative(ℤ/13915)ˣ, (ℤ/27830)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C5×C112
socle, prime radicalC23×C5×C112C2
LCSG ▷ C1
UCSC1 ◁ G

756 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C8×C112, C2×C42×C5×C112, C23×C4×C5×C112, …
maximal normal subgroup ofC22×C5×C8×C112, C2×C42×C5×C112, C23×C4×C5×C112, …
maximal quotient ofC22×C5×C8×C112, C2×C42×C5×C112, C23×C4×C5×C112, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.