Finite Group Databasebeta

← Prev (#30651942) Next (#30651944) →

2−1+4×Dic127 #30651943

order16256
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×Dic127

Splittings

SylowC127 ⋊ C4×2−1+4

Subgroups

subgroupG/H
center, FrattiniC22C24×D127
commutatorC2×C127C24×C4
Fitting, prime radicalC2×2−1+4×C127C2
socle, cosocleC22×C127C25
hypercenterC2×2−1+4D127
hypocenterC127C4×2−1+4
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C2×2−1+4

1492 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.

normal subgroups only

This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 1063 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

2210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 17723);