Finite Group Databasebeta

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C2×#31799873 #47985576

order35456
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#31799873

Splittings

FittingC22×C4⋊C4×C277 ⋊ C2
SylowC277 ⋊ C2×#385

Subgroups

subgroupG/H
centerC24C22×D277
commutatorC22×C277C23×C4
FrattiniC23C23×D277
FittingC22×C4⋊C4×C277C2
socleC24×C277C23
prime radicalC24×D277C22
cosocleC23×C277C24
hypercenterC22×C4⋊C4D277
hypocenterC277C2×#385
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C24 ◁ C22×C4⋊C4

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17728

Conjugacy classes & character table

5576 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35456, 6919);