Finite Group Databasebeta

C2×#21422913 #28558080

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21422913

Splittings

SylowC59 ⋊ C2×#1579

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D59
commutatorC4×C59C23×C8
FrattiniC42C23×D59
FittingC2×C8×Q8×C59C2
socle, prime radicalC23×C59C4×D4
cosocleC42×C59C24
hypercenterC2×C8×Q8D59
hypocenterC59C2×#1579
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C8×Q8

718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 138959);