Finite Group Databasebeta

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C2×C4×C4⋊Dic277 #47985502

order35456
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C4⋊Dic277

Splittings

SylowC277 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D277
commutatorC2×C277C22×C42
FrattiniC23C23×D277
FittingC22×C42×C277C2
socle, prime radicalC24×C277C23
cosocleC23×C277C24
hypercenterC22×C42D277
hypocenterC277C2×C4×C4⋊C4
LCSG ▷ C2×C277 ▷ C277
UCSC1 ◁ C23×C4 ◁ C22×C42

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35456

Conjugacy classes & character table

8912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35456, 6845);