Finite Group Databasebeta

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C22×C4×C11×C79 #72192122

order13904
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 149760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C11×C79
multiplicative(ℤ/21873)ˣ, (ℤ/29164)ˣ, (ℤ/43746)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C11×C79
socle, prime radicalC23×C11×C79C2
LCSG ▷ C1
UCSC1 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13904 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C42×C11×C79, C22×C8×C11×C79, C23×C4×C11×C79
maximal normal subgroup ofC2×C42×C11×C79, C22×C8×C11×C79, C23×C4×C11×C79
maximal quotient ofC2×C42×C11×C79, C22×C8×C11×C79, C23×C4×C11×C79

GAP

Past the SmallGroups library coverage — no SmallGroups id.