Finite Group Databasebeta

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C2×C4×#16838749 #44509781

order30848
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#16838749

Splittings

SylowC241 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D241
commutatorC2×C241C22×C42
FrattiniC23C23×D241
FittingC22×C42×C241C2
socle, prime radicalC24×C241C23
cosocleC23×C241C24
hypercenterC22×C42D241
hypocenterC241C2×C4×C4⋊C4
LCSG ▷ C2×C241 ▷ C241
UCSC1 ◁ C23×C4 ◁ C22×C42

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30848

Conjugacy classes & character table

7760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 6846);