Finite Group Databasebeta

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C22×C42×C5×C37 #72190291

order11840
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 21233664
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4

Aliases

abelianC22×C42×C5×C37
multiplicative(ℤ/24585)ˣ, (ℤ/26224)ˣ, (ℤ/29800)ˣ, (ℤ/32780)ˣ, (ℤ/44700)ˣ, (ℤ/49170)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C24×C5×C37
socle, prime radicalC24×C5×C37C22
LCSG ▷ C1
UCSC1 ◁ G

996 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C5×C8×C37, C2×C43×C5×C37, C23×C42×C5×C37
maximal normal subgroup ofC22×C4×C5×C8×C37, C2×C43×C5×C37, C23×C42×C5×C37
maximal quotient ofC22×C4×C5×C8×C37, C2×C43×C5×C37, C23×C42×C5×C37
automorphism group ofC11×C16×C149, C8×C25×C149
outer automorphism group ofC11×C16×C149, C8×C25×C149

GAP

Past the SmallGroups library coverage — no SmallGroups id.