Finite Group Databasebeta

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C22×C5×C8×C37 #72185137

order5920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 55296
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C5×C8×C37
multiplicative(ℤ/11848)ˣ, (ℤ/17772)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C23×C5×C37
socle, prime radicalC23×C5×C37C4
LCSG ▷ C1
UCSC1 ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C16×C37, C2×C4×C5×C8×C37, C23×C5×C8×C37, …
maximal normal subgroup ofC22×C5×C16×C37, C2×C4×C5×C8×C37, C23×C5×C8×C37, …
maximal quotient ofC22×C5×C16×C37, C2×C4×C5×C8×C37, C23×C5×C8×C37, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.