Finite Group Databasebeta

C2×#14272095 #16835912

order3712
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14272095

Splittings

SylowC29 ⋊ C2×M64

Subgroups

subgroupG/H
centerC2×C8C2×#1181
commutatorC2×C29C22×C16
FrattiniC8C22×#1181
FittingC22×C8×C29C4
socleC22×C29C2×C16
prime radicalC23×C29C16
cosocle#90768C23
hypercenterC22×C8#1181
hypocenterC29C2×M64
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C8 ◁ C22×C8

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 20930);