Finite Group Databasebeta

C22×(C2×D307)⋊C4 #34088334

order19648
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D307)⋊C4

Splittings

FittingC23×C4×C307 ⋊ C2
SylowC307 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D307
commutatorC2×C307C23×C4
FrattiniC22C23×D307
FittingC23×C4×C307C2
socleC24×C307C22
prime radicalC24×D307C2
cosocleC22×C307C24
hypercenterC23×C4D307
hypocenterC307C22×C22⋊C4
LCSG ▷ C2×C307 ▷ C307
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9824

Conjugacy classes & character table

4936 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19648, 996);