Finite Group Databasebeta

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C2×C4⋊C4×#3622 #17032254

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4⋊C4×#3622

Splittings

SylowC17 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC2×C17C22×C4×C8
FrattiniC22×C4C23×D17
FittingC2×C4×C4⋊C4×C17C2
socle, prime radicalC24×C17C22×C4
cosocleC22×C4×C17C24
hypercenterC2×C4×C4⋊C4D17
hypocenterC17C2×C8×C4⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 167498);