Finite Group Databasebeta

C2×#21421933 #28478181

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21421933

Splittings

SylowC59 ⋊ C2×#1278

Subgroups

subgroupG/H
centerC2×C42D236
commutatorC4×C59C2×C4×C8
FrattiniC2×C42C22×D59
FittingC22×C4×C8×C59C2
socleC23×C59#95
prime radicalC24×C59C4⋊C4
cosocleC2×C42×C59C23
hypercenterC22×C4×C8D59
hypocenterC59C2×#1278
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C22×C4×C8

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3824 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 59060);