Finite Group Databasebeta

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C2×C4×Dic239⋊C4 #44486884

order30592
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×Dic239⋊C4

Splittings

SylowC239 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D239
commutatorC2×C239C22×C42
FrattiniC23C23×D239
FittingC22×C42×C239C2
socle, prime radicalC24×C239C23
cosocleC23×C239C24
hypercenterC22×C42D239
hypocenterC239C2×C4×C4⋊C4
LCSG ▷ C2×C239 ▷ C239
UCSC1 ◁ C23×C4 ◁ C22×C42

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30592

Conjugacy classes & character table

7696 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 6846);