Finite Group Databasebeta

C2×#14524050 #16864159

order4288
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14524050

Splittings

SylowC67 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D67
commutatorC2×C67C23×C4
FrattiniC4C23×D67
Fitting, prime radicalC2×#41×C67C2
socleC22×C67C22×C4
cosocleC4×C67C24
hypercenterC2×#41D67
hypocenterC67C2×#131
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4288, 1312);