Finite Group Databasebeta

C2×D4⋊#11924003 #32995683

order18688
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×D4⋊#11924003

Splittings

SylowC73 ⋊ C2×D4⋊C16

Subgroups

subgroupG/H
centerC22×C8C22⋊D73
commutatorC4×C73C22×C16
FrattiniC4×C8C22×D73
FittingC2×C8×D4×C73C2
socleC23×C73C22⋊C8
prime radicalC22×D4×C73C8
cosocleC4×C8×C73C23
hypercenterC2×C8×D4D73
hypocenterC73C2×D4⋊C16
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C8×D4

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

2992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 79267);