Finite Group Databasebeta

SD16×C199⋊C8 #38767651

order25472
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productSD16×C199⋊C8

Splittings

SylowC199 ⋊ C8×SD16

Subgroups

subgroupG/H
centerC2×C4D4×D199
commutatorC4×C199C22×C8
FrattiniC42C22×D199
FittingC4×SD16×C199C2
socleC22×C199C4×D4
prime radicalC2×D4×C199C2×C4
cosocleC42×C199C23
hypercenterC4×SD16D199
hypocenterC199C8×SD16
LCSG ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

180 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 89 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) = 12736

Conjugacy classes & character table

2828 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25472, 3311);