Finite Group Databasebeta

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C2×C3×C4×C5×C127 #72193262

order15240
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8064
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C4×C5×C127
multiplicative(ℤ/15779)ˣ, (ℤ/22863)ˣ, (ℤ/30484)ˣ, (ℤ/31558)ˣ, (ℤ/45726)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C5×C127
socle, prime radicalC22×C3×C5×C127C2
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15240 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C8×C127, C3×C42×C5×C127, C22×C3×C4×C5×C127
maximal normal subgroup ofC2×C3×C5×C8×C127, C3×C42×C5×C127, C22×C3×C4×C5×C127
maximal quotient ofC2×C3×C5×C8×C127, C3×C42×C5×C127, C22×C3×C4×C5×C127
automorphism group ofC31×C509
outer automorphism group ofC31×C509

GAP

Past the SmallGroups library coverage — no SmallGroups id.