Finite Group Databasebeta

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C4×C5×C8×C67 #72189263

order10720
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 33792
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C5×C8×C67
multiplicative(ℤ/11029)ˣ, (ℤ/22058)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C22×C5×C67
socle, prime radicalC22×C5×C67C2×C4
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C16×C67, C5×C82×C67, C2×C4×C5×C8×C67, …
maximal normal subgroup ofC4×C5×C16×C67, C5×C82×C67, C2×C4×C5×C8×C67, …
maximal quotient ofC4×C5×C16×C67, C5×C82×C67, C2×C4×C5×C8×C67, …
automorphism group ofC41×C269
outer automorphism group ofC41×C269

GAP

Past the SmallGroups library coverage — no SmallGroups id.