Finite Group Databasebeta

C2×Q16×Dic118 #29469138

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×Q16×Dic118

Splittings

SylowC59 ⋊ C2×Q8×Q16

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×Q16×C59C2
socle, prime radicalC23×C59C22×D4
hypercenterC2×C4×Q16D59
hypocenterC59C2×Q8×Q16
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

1830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1050017);