Finite Group Databasebeta

C2×Dic388 #15690828

order3104
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic388

Splittings

SylowC97 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22D388
commutator, cosocleC4×C97C23
FrattiniC4C22×D97
FittingC2×C8×C97C2
socle, prime radicalC22×C97D4
hypercenterC2×C8D97
hypocenterC97C2×Q16
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3104

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3104, 164);