Finite Group Databasebeta

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C2×C3×C4×C13×C37 #72189990

order11544
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6912
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C4×C13×C37
multiplicative(ℤ/11771)ˣ, (ℤ/11819)ˣ, (ℤ/14435)ˣ, (ℤ/23542)ˣ, (ℤ/23638)ˣ, (ℤ/28870)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C13×C37
socle, prime radicalC22×C3×C13×C37C2
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11544 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C8×C13×C37, C3×C42×C13×C37, C22×C3×C4×C13×C37
maximal normal subgroup ofC2×C3×C8×C13×C37, C3×C42×C13×C37, C22×C3×C4×C13×C37
maximal quotient ofC2×C3×C8×C13×C37, C3×C42×C13×C37, C22×C3×C4×C13×C37
automorphism group ofC79×C149, C53×C223, C5×C2887
outer automorphism group ofC79×C149, C53×C223, C5×C2887

GAP

Past the SmallGroups library coverage — no SmallGroups id.