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C4⋊C4×D764 #37575423

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×D764

Splittings

FittingC4×C4⋊C4×C191 ⋊ C2
SylowC191 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
FittingC4×C4⋊C4×C191C2
socle, cosocleC23×C191C24
prime radicalC22×D764C22
hypercenterC4×C4⋊C4D191
hypocenterC191D4×C4⋊C4
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ C4×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

3850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 7413);