Finite Group Databasebeta

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C2×C32×C4×C7×C23 #72190031

order11592
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 50688
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC2×C32×C4×C7×C23
multiplicative(ℤ/11911)ˣ, (ℤ/12571)ˣ, (ℤ/13531)ˣ, (ℤ/13573)ˣ, (ℤ/17397)ˣ, (ℤ/23822)ˣ, (ℤ/25142)ˣ, (ℤ/27062)ˣ, (ℤ/27146)ˣ, (ℤ/34794)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C32×C7×C23
socle, prime radicalC22×C32×C7×C23C2
LCSG ▷ C1
UCSC1 ◁ G

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11592 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C7×C8×C23, C32×C42×C7×C23, C22×C32×C4×C7×C23
maximal normal subgroup ofC2×C32×C7×C8×C23, C32×C42×C7×C23, C22×C32×C4×C7×C23
maximal quotient ofC2×C32×C7×C8×C23, C32×C42×C7×C23, C22×C32×C4×C7×C23
automorphism group ofC43×C277, C13×C967, C7×C1933
outer automorphism group ofC43×C277, C13×C967, C7×C1933

GAP

Past the SmallGroups library coverage — no SmallGroups id.