Finite Group Databasebeta

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C2×C3×C32×C37 #72186154

order7104
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C32×C37

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C22×C3×C37
socle, prime radicalC22×C3×C37C16
LCSG ▷ C1
UCSC1 ◁ G

68 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7104 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C37×C64, C3×C4×C32×C37, C22×C3×C32×C37, …
maximal normal subgroup ofC2×C3×C37×C64, C3×C4×C32×C37, C22×C3×C32×C37, …
maximal quotient ofC2×C3×C37×C64, C3×C4×C32×C37, C22×C3×C32×C37, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.