Finite Group Databasebeta

C2×#14561546 #18072921

order4864
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#14561546

Splittings

SylowC19 ⋊ C2×#1307

Subgroups

subgroupG/H
centerC23C19⋊#95
commutatorC23×C19C2×C42
FrattiniC2×C42C22×D19
FittingC2×C19×#423C2
socleC23×C19#95
prime radicalC24×C19C42
cosocleC2×C42×C19C23
hypercenterC2×#423D19
hypocenterC19C2×#1307
LCSG ▷ C23×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 59950);