Finite Group Databasebeta

D4×D37⋊C8 #18011299

order4736
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productD4×D37⋊C8
unambiguous semidirect productD37⋊(C8×D4)

Splittings

SylowC37 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC2×C4C22×#3866
commutatorC2×C37C23×C8
FrattiniC22C23×#3866
FittingC4×D4×C37C4
socleC22×C37C23×C4
prime radicalC2×D4×D37C4
cosocleC2×Dic37C24
hypercenterC4×D4#3866
hypocenterC37C2×C8×D4
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C4×D4

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1184

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 21213);