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C2×C3×C5×C8×C37 #72187708

order8880
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C5×C8×C37
multiplicative(ℤ/9143)ˣ, (ℤ/10367)ˣ, (ℤ/13323)ˣ, (ℤ/13329)ˣ, (ℤ/17764)ˣ, (ℤ/18286)ˣ, (ℤ/20734)ˣ, (ℤ/26646)ˣ, (ℤ/26658)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C3×C5×C37
socle, prime radicalC22×C3×C5×C37C4
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8880 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C16×C37, C3×C4×C5×C8×C37, C22×C3×C5×C8×C37, …
maximal normal subgroup ofC2×C3×C5×C16×C37, C3×C4×C5×C8×C37, C22×C3×C5×C8×C37, …
maximal quotient ofC2×C3×C5×C16×C37, C3×C4×C5×C8×C37, C22×C3×C5×C8×C37, …
automorphism group ofC41×C223, C7×C1481, C3×C4441
outer automorphism group ofC41×C223, C7×C1481, C3×C4441

GAP

Past the SmallGroups library coverage — no SmallGroups id.