Finite Group Databasebeta

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C23×C32×C4×C52 #72186278

order7200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 495452160
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3×C5

Aliases

abelianC23×C32×C4×C52
multiplicative(ℤ/11935)ˣ, (ℤ/13299)ˣ, (ℤ/14091)ˣ, (ℤ/15128)ˣ, (ℤ/15345)ˣ, (ℤ/16275)ˣ, (ℤ/17325)ˣ, (ℤ/17732)ˣ, (ℤ/18788)ˣ, (ℤ/21700)ˣ, (ℤ/22692)ˣ, (ℤ/23870)ˣ, (ℤ/24156)ˣ, (ℤ/26598)ˣ, (ℤ/27900)ˣ, (ℤ/28182)ˣ, (ℤ/30690)ˣ, (ℤ/32550)ˣ, (ℤ/34650)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C32×C52
socle, prime radicalC24×C32×C52C2
LCSG ▷ C1
UCSC1 ◁ G

5664 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C32×C52×C8, C22×C32×C42×C52, C24×C32×C4×C52, …
maximal normal subgroup ofC23×C32×C52×C8, C22×C32×C42×C52, C24×C32×C4×C52, …
maximal quotient ofC23×C32×C52×C8, C22×C32×C42×C52, C24×C32×C4×C52, …
automorphism group ofC8×C31×C61
outer automorphism group ofC8×C31×C61

GAP

Past the SmallGroups library coverage — no SmallGroups id.