Finite Group Databasebeta

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C2×C3×C8×C227 #72189441

order10896
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7232
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C8×C227
multiplicative(ℤ/16347)ˣ, (ℤ/21796)ˣ, (ℤ/32694)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C3×C227
socle, prime radicalC22×C3×C227C4
LCSG ▷ C1
UCSC1 ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10896 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C16×C227, C3×C4×C8×C227, C22×C3×C8×C227, …
maximal normal subgroup ofC2×C3×C16×C227, C3×C4×C8×C227, C22×C3×C8×C227, …
maximal quotient ofC2×C3×C16×C227, C3×C4×C8×C227, C22×C3×C8×C227, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.