Finite Group Databasebeta

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C2×C4×#10587575 #17192811

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×C4×#10587575

Splittings

SylowC17 ⋊ C2×C4×#125

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C4×C4⋊C4×C17C2
socle, prime radicalC24×C17C24
cosocleC23×C17C25
hypercenterC2×C4×C4⋊C4D17
hypocenterC17C2×C4×#125
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 328055);