Finite Group Databasebeta

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C2×C4⋊C4×Dic29 #16821829

order3712
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4⋊C4×Dic29

Splittings

SylowC29 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×D29
commutatorC2×C29C22×C42
FrattiniC23C23×D29
FittingC22×C4⋊C4×C29C2
socle, prime radicalC24×C29C23
cosocleC23×C29C24
hypercenterC22×C4⋊C4D29
hypocenterC29C2×C4×C4⋊C4
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C24 ◁ C22×C4⋊C4

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 6847);