Finite Group Databasebeta

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C4×#11715828 #72341272

order3072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#11715828

Splittings

FittingC4×H(7,𝔽2) ⋊ D3

Subgroups

subgroupG/H
centerC2×C4C22×#1020
commutator, hypocenter#997C23×C4
Frattini, socleC22C23×#1020
FittingC4×H(7,𝔽2)D3
prime radicalC2×#11715828C2
cosocleC2×#997C24
hypercenterC4×D4#1020
LCSG ▷ #997
UCSC1 ◁ C2×C4 ◁ C4×D4

At least 6703 conjugacy classes of subgroups; only the 258 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#72217027
maximal normal subgroup ofC4×#72217027

GAP

Past the SmallGroups library coverage — no SmallGroups id.