Finite Group Databasebeta

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C22×C4×C25×C29 #72190040

order11600
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 107520
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C25×C29
multiplicative(ℤ/17877)ˣ, (ℤ/21765)ˣ, (ℤ/22125)ˣ, (ℤ/23216)ˣ, (ℤ/23836)ˣ, (ℤ/29020)ˣ, (ℤ/29500)ˣ, (ℤ/35754)ˣ, (ℤ/43530)ˣ, (ℤ/44250)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C5C23×C5×C29
socle, prime radicalC23×C5×C29C2×C5
LCSG ▷ C1
UCSC1 ◁ G

162 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C8×C25×C29, C2×C42×C25×C29, C23×C4×C25×C29
maximal normal subgroup ofC22×C8×C25×C29, C2×C42×C25×C29, C23×C4×C25×C29
maximal quotient ofC22×C8×C25×C29, C2×C42×C25×C29, C23×C4×C25×C29
automorphism group ofC3×C59×C125, C4×C59×C125
outer automorphism group ofC3×C59×C125, C4×C59×C125

GAP

Past the SmallGroups library coverage — no SmallGroups id.