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C2×C5×C7×C8×C27 #72193147

order15120
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6912
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C5×C7×C8×C27
multiplicative(ℤ/15539)ˣ, (ℤ/22683)ˣ, (ℤ/22761)ˣ, (ℤ/30244)ˣ, (ℤ/31078)ˣ, (ℤ/45366)ˣ, (ℤ/45522)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C9C22×C3×C5×C7
socle, prime radicalC22×C3×C5×C7C4×C9
LCSG ▷ C1
UCSC1 ◁ G

176 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C7×C16×C27, C4×C5×C7×C8×C27, C22×C5×C7×C8×C27
maximal normal subgroup ofC2×C5×C7×C16×C27, C4×C5×C7×C8×C27, C22×C5×C7×C8×C27
maximal quotient ofC2×C5×C7×C16×C27, C4×C5×C7×C8×C27, C22×C5×C7×C8×C27
automorphism group ofC41×C379
outer automorphism group ofC41×C379

GAP

Past the SmallGroups library coverage — no SmallGroups id.