Finite Group Databasebeta

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C23×C3×C4×C52×C9 #72199111

order21600
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1114767360
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3×C5

Aliases

abelianC23×C3×C4×C52×C9
multiplicative(ℤ/32395)ˣ, (ℤ/36575)ˣ, (ℤ/37851)ˣ, (ℤ/38247)ˣ, (ℤ/41811)ˣ, (ℤ/44175)ˣ, (ℤ/44888)ˣ, (ℤ/46035)ˣ, (ℤ/47025)ˣ, (ℤ/50468)ˣ, (ℤ/50996)ˣ, (ℤ/51975)ˣ, (ℤ/55748)ˣ, (ℤ/58900)ˣ, (ℤ/64790)ˣ, (ℤ/67332)ˣ, (ℤ/71676)ˣ, (ℤ/72468)ˣ, (ℤ/73150)ˣ, (ℤ/75702)ˣ, (ℤ/76494)ˣ, (ℤ/83622)ˣ, (ℤ/83700)ˣ, (ℤ/88350)ˣ, (ℤ/92070)ˣ, (ℤ/94050)ˣ, (ℤ/103950)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C24×C32×C52
socle, prime radicalC24×C32×C52C2×C3
LCSG ▷ C1
UCSC1 ◁ G

9440 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

21600 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.