Finite Group Databasebeta

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C2×C3×C112×C16 #72190050

order11616
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 844800
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C11

Aliases

abelianC2×C3×C112×C16

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C22×C3×C112
socle, prime radicalC22×C3×C112C8
LCSG ▷ C1
UCSC1 ◁ G

392 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C112×C32, C3×C4×C112×C16, C22×C3×C112×C16
maximal normal subgroup ofC2×C3×C112×C32, C3×C4×C112×C16, C22×C3×C112×C16
maximal quotient ofC2×C3×C112×C32, C3×C4×C112×C16, C22×C3×C112×C16

GAP

Past the SmallGroups library coverage — no SmallGroups id.