Finite Group Databasebeta

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C2×C32×C52×C32 #72192545

order14400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1474560
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3×C5

Aliases

abelianC2×C32×C52×C32

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C22×C32×C52
socle, prime radicalC22×C32×C52C16
LCSG ▷ C1
UCSC1 ◁ G

816 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C52×C64, C32×C4×C52×C32, C22×C32×C52×C32
maximal normal subgroup ofC2×C32×C52×C64, C32×C4×C52×C32, C22×C32×C52×C32
maximal quotient ofC2×C32×C52×C64, C32×C4×C52×C32, C22×C32×C52×C32

GAP

Past the SmallGroups library coverage — no SmallGroups id.