Finite Group Databasebeta

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C4⋊C8×Dic107 #28336312

order13696
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C8×Dic107

Splittings

SylowC107 ⋊ C4×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×D107
commutatorC2×C107C2×C4×C8
FittingC2×C4⋊C8×C107C2
socle, prime radicalC23×C107C22×C4
cosocleC22×C4×C107C23
hypercenterC2×C4⋊C8D107
hypocenterC107C4×C4⋊C8
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

316 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 177 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) = 13696

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 4361);