Finite Group Databasebeta

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C23×C3×C4×C5×C29 #72192135

order13920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4816896
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C4×C5×C29
multiplicative(ℤ/22715)ˣ, (ℤ/25311)ˣ, (ℤ/27435)ˣ, (ℤ/28792)ˣ, (ℤ/29205)ˣ, (ℤ/29264)ˣ, (ℤ/30712)ˣ, (ℤ/30975)ˣ, (ℤ/33748)ˣ, (ℤ/36580)ˣ, (ℤ/41300)ˣ, (ℤ/41784)ˣ, (ℤ/43188)ˣ, (ℤ/45430)ˣ, (ℤ/46068)ˣ, (ℤ/50622)ˣ, (ℤ/53100)ˣ, (ℤ/54870)ˣ, (ℤ/58410)ˣ, (ℤ/61950)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C3×C5×C29
socle, prime radicalC24×C3×C5×C29C2
LCSG ▷ C1
UCSC1 ◁ G

944 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C5×C8×C29, C22×C3×C42×C5×C29, C24×C3×C4×C5×C29
maximal normal subgroup ofC23×C3×C5×C8×C29, C22×C3×C42×C5×C29, C24×C3×C4×C5×C29
maximal quotient ofC23×C3×C5×C8×C29, C22×C3×C42×C5×C29, C24×C3×C4×C5×C29
automorphism group ofC8×C59×C61, C16×C31×C59, C8×C11×C349
outer automorphism group ofC8×C59×C61, C16×C31×C59, C8×C11×C349

GAP

Past the SmallGroups library coverage — no SmallGroups id.