Finite Group Databasebeta

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C2×C4×C5×C8×C23 #72186377

order7360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 180224
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C4×C5×C8×C23
multiplicative(ℤ/9635)ˣ, (ℤ/14752)ˣ, (ℤ/19270)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C23×C5×C23
socle, prime radicalC23×C5×C23C2×C4
LCSG ▷ C1
UCSC1 ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C5×C16×C23, C2×C5×C82×C23, C42×C5×C8×C23, …
maximal normal subgroup ofC2×C4×C5×C16×C23, C2×C5×C82×C23, C42×C5×C8×C23, …
maximal quotient ofC2×C4×C5×C16×C23, C2×C5×C82×C23, C42×C5×C8×C23, …
automorphism group ofC5×C41×C47
outer automorphism group ofC5×C41×C47

GAP

Past the SmallGroups library coverage — no SmallGroups id.