Finite Group Databasebeta

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C4×#21440641 #44510015

order30848
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#21440641

Splittings

SylowC241 ⋊ C4×C4⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D241
commutatorC22×C241C23×C4
FrattiniC23C23×D241
FittingC4×C4⋊C4×C241C2
socle, prime radical, cosocleC23×C241C24
hypercenterC4×C4⋊C4D241
hypocenterC241C4×C4⋊Q8
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30848

Conjugacy classes & character table

4856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 7080);