Finite Group Databasebeta

D4×#14556654 #34026132

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#14556654

Splittings

FittingD4×Q8×C73 ⋊ C4
SylowC73 ⋊ D4×#103

Subgroups

subgroupG/H
centerC22C22×C22⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingD4×Q8×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC2×D4×D73D4
cosocleC2×C4×D73C24
hypercenterD4×Q8#64408
hypocenterC73D4×#103
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

1530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1109716);