Finite Group Databasebeta

C2×Q8×Dic236 #29469139

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

Aliases

direct productC2×Q8×Dic236

Splittings

SylowC59 ⋊ C2×Q8×Q16

Subgroups

subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C8×Q8×C59C2
socle, prime radicalC23×C59C22×D4
hypercenterC2×C8×Q8D59
hypocenterC59C2×Q8×Q16
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

1830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1050018);