Finite Group Databasebeta

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C4×C4⋊C4×D241 #44509778

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

Aliases

direct productC4×C4⋊C4×D241

Splittings

FittingC4×C4⋊C4×C241 ⋊ C2
SylowC241 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C22×D241
commutatorC2×C241C22×C42
FrattiniC23C23×D241
FittingC4×C4⋊C4×C241C2
socle, cosocleC23×C241C24
prime radicalC23×D241C23
hypercenterC4×C4⋊C4D241
hypocenterC241C2×C4×C4⋊C4
LCSG ▷ C2×C241 ▷ C241
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15424

Conjugacy classes & character table

4880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 6843);