Finite Group Databasebeta

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D4×#72210302 #72259477

order32448
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#72210302

Splittings

FittingD4×C132 ⋊ C2×C3×C4
HallD4×D13⋊#261 ⋊ C3
Hall#92788 ⋊ C2×C4×D4
SylowC132 ⋊ C2×C3×C4×D4

Subgroups

subgroupG/H
center, FrattiniC2C22×#72210302
commutator, socleC2×C132C23×C3×C4
FittingD4×C132C2×C3×C4
prime radicalD4×#11759815⋊C2C2
cosocleC2×C13⋊D13C24×C3
hypercenterD4#72210302
hypocenterC132C2×C3×C4×D4
LCSG ▷ C2×C132 ▷ C132
UCSC1 ◁ C2 ◁ D4

2268 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 104

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.