Finite Group Databasebeta

D4×C4⋊Dic191 #37575422

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

Aliases

direct productD4×C4⋊Dic191

Splittings

SylowC191 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
FittingC2×C4×D4×C191C2
socle, cosocleC23×C191C24
prime radicalC22×D4×C191C22
hypercenterC2×C4×D4D191
hypocenterC191D4×C4⋊C4
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ C2×C4×D4

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, 7412);