Finite Group Databasebeta

C2×#21422074 #28498487

order15104
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21422074

Splittings

SylowC59 ⋊ C2×Q8⋊C16

Subgroups

subgroupG/H
centerC22×C8C22⋊D59
commutatorC4×C59C22×C16
FrattiniC4×C8C22×D59
FittingC2×C59×C4⋊C16C2
socle, prime radicalC23×C59C22⋊C8
cosocleC4×C8×C59C23
hypercenterC2×C4⋊C16D59
hypocenterC59C2×Q8⋊C16
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C4⋊C16

382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 79366);