Finite Group Databasebeta

← Prev (#72219141) Next (#72219143) →

C2×C3×C4×D52 #72219142

order2400
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×C4×D52

Splittings

FittingC2×C3×C4×C52 ⋊ C22
derived, SylowC52 ⋊ C23×C3×C4
HallC3×C52 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4D52
commutator, hypocenterC52C23×C3×C4
FrattiniC2C22×C3×D52
FittingC2×C3×C4×C52C22
socleC22×C3×C52C23
prime radicalC22×C3×D52C2
cosocleC2×C52C24×C3
LCSG ▷ C52
UCSC1 ◁ C2×C3×C4

1052 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3×D5×#6732

GAP

Past the SmallGroups library coverage — no SmallGroups id.