Finite Group Databasebeta

C2×C4×Dic436 #28371798

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic436

Splittings

SylowC109 ⋊ C2×C4×Q16

Subgroups

subgroupG/H
centerC22×C4D436
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
FittingC2×C4×C8×C109C2
socle, prime radicalC23×C109C2×D4
cosocleC2×C4×C109C24
hypercenterC2×C4×C8D109
hypocenterC109C2×C4×Q16
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

488 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

Conjugacy classes & character table

3512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13276);