Finite Group Databasebeta

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C4×#17985749 #31888634

order18176
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#17985749

Splittings

SylowC71 ⋊ C4×#334

Subgroups

subgroupG/H
centerC2×C42C22⋊D71
commutatorC4×C71C2×C4×C8
FrattiniC2×C42C22×D71
FittingC4×C4⋊C8×C71C2
socle, prime radicalC23×C71C2×C4⋊C4
cosocleC2×C42×C71C23
hypercenterC4×C4⋊C8D71
hypocenterC71C4×#334
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C42 ◁ C43 ◁ C4×C4⋊C8

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18176

Conjugacy classes & character table

2912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 60750);