Finite Group Databasebeta

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C4×#20259302 #37575057

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#20259302

Splittings

FittingC4×C4⋊C4×C191 ⋊ C2
SylowC191 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D191
commutatorC22×C191C23×C4
FrattiniC23C23×D191
FittingC4×C4⋊C4×C191C2
socle, cosocleC23×C191C24
prime radicalC23×D191C23
hypercenterC4×C4⋊C4D191
hypocenterC191C4×C22⋊Q8
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

3856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 7047);