Finite Group Databasebeta

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C22×C3×C4×C151 #72186306

order7248
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 57600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C151
multiplicative(ℤ/13605)ˣ, (ℤ/14512)ˣ, (ℤ/18140)ˣ, (ℤ/27210)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C151
socle, prime radicalC23×C3×C151C2
LCSG ▷ C1
UCSC1 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7248 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C42×C151, C22×C3×C8×C151, C23×C3×C4×C151, …
maximal normal subgroup ofC2×C3×C42×C151, C22×C3×C8×C151, C23×C3×C4×C151, …
maximal quotient ofC2×C3×C42×C151, C22×C3×C8×C151, C23×C3×C4×C151, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.