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#117×Dic11 #13070959

order1408
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×Dic11

Splittings

SylowC11 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D11
commutatorC2×C11C22×C42
FrattiniC23C23×D11
FittingC2×C11×#117C2
socle, cosocleC23×C11C24
prime radicalC24×C11C23
hypercenterC2×#117D11
hypocenterC11C4×#117
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#117

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

Relationships

maximal subgroup of#14647214, #14647218, Dic11×H(3,ℤ/4), …
maximal normal subgroup of#14647214, #14647218, Dic11×H(3,ℤ/4), …
maximal quotient ofDic11×#376, C4×C22⋊C4×Dic11, C4×C4⋊C4×Dic11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 6853);