Finite Group Databasebeta

C4×Dic172 #14582995

order2752
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic172

Splittings

SylowC43 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC2×C4D172
commutatorC4×C43C22×C4
FrattiniC2×C4C22×D43
FittingC4×C8×C43C2
socle, prime radicalC22×C43C2×D4
cosocleC2×C4×C43C23
hypercenterC4×C8D43
hypocenterC43C4×Q16
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2752

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(2752, 645);