Finite Group Databasebeta

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C4×#22579860 #47985704

order35456
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#22579860

Splittings

FittingC4×C4⋊C4×C277 ⋊ C2
SylowC277 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D277
commutatorC22×C277C23×C4
FrattiniC23C23×D277
FittingC4×C4⋊C4×C277C2
socle, cosocleC23×C277C24
prime radicalC23×D277C23
hypercenterC4×C4⋊C4D277
hypocenterC277C4×C22⋊Q8
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

656 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, 7047);