Finite Group Databasebeta

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C22×C4×C5×C67 #72184672

order5360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 50688
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C5×C67
multiplicative(ℤ/8877)ˣ, (ℤ/11836)ˣ, (ℤ/17754)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C5×C67
socle, prime radicalC23×C5×C67C2
LCSG ▷ C1
UCSC1 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C8×C67, C2×C42×C5×C67, C23×C4×C5×C67, …
maximal normal subgroup ofC22×C5×C8×C67, C2×C42×C5×C67, C23×C4×C5×C67, …
maximal quotient ofC22×C5×C8×C67, C2×C42×C5×C67, C23×C4×C5×C67, …
automorphism group ofC3×C11×C269
outer automorphism group ofC3×C11×C269

GAP

Past the SmallGroups library coverage — no SmallGroups id.