Finite Group Databasebeta

Q16×C4⋊Dic61 #29698445

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ16×C4⋊Dic61

Splittings

SylowC61 ⋊ C4⋊C4×Q16

Subgroups

subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×Q16×C61C2
socle, prime radicalC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×C4×Q16D61
hypocenterC61C4⋊C4×Q16
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 188000);