Finite Group Databasebeta

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C2×#14272114 #16835947

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14272114
unambiguous semidirect productD29⋊#389

Splittings

FittingC2×C4⋊C4×C29 ⋊ C4
SylowC29 ⋊ C2×#389

Subgroups

subgroupG/H
centerC23C22×#1181
commutatorC22×C29C23×C4
FrattiniC22C23×#1181
FittingC2×C4⋊C4×C29C4
socleC23×C29C22×C4
prime radicalC23×D29C23
cosocleC22×D29C24
hypercenterC2×C4⋊C4#1181
hypocenterC29C2×#389
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×C4⋊C4

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 20965);