Finite Group Databasebeta

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C2×C3×C4×C16×C23 #72187679

order8832
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 180224
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C4×C16×C23
multiplicative(ℤ/10387)ˣ, (ℤ/11815)ˣ, (ℤ/14127)ˣ, (ℤ/17728)ˣ, (ℤ/18836)ˣ, (ℤ/20774)ˣ, (ℤ/23630)ˣ, (ℤ/28254)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C23×C3×C23
socle, prime radicalC23×C3×C23C2×C8
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8832 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C23×C32, C3×C42×C16×C23, C2×C3×C8×C16×C23, …
maximal normal subgroup ofC2×C3×C4×C23×C32, C3×C42×C16×C23, C2×C3×C8×C16×C23, …
maximal quotient ofC2×C3×C4×C23×C32, C3×C42×C16×C23, C2×C3×C8×C16×C23, …
automorphism group ofC13×C17×C47, C5×C17×C139
outer automorphism group ofC13×C17×C47, C5×C17×C139

GAP

Past the SmallGroups library coverage — no SmallGroups id.