Finite Group Databasebeta

D4×#14272345 #28417461

order14912
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD4×#14272345

Splittings

SylowC233 ⋊ C8×D4

Subgroups

subgroupG/H
center, FrattiniC22C22×#11745400
commutatorC2×C233C22×C8
Fitting, prime radicalC2×D4×C233C4
socleC22×C233C22×C4
cosocleC2×Dic233C23
hypercenterC2×D4#11745400
hypocenterC233C8×D4
LCSG ▷ C2×C233 ▷ C233
UCSC1 ◁ C22 ◁ C2×D4

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7456

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 1575);