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#117×Dic17 #14531127

order2176
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×Dic17

Splittings

SylowC17 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D17
commutatorC2×C17C22×C42
FrattiniC23C23×D17
FittingC2×C17×#117C2
socle, cosocleC23×C17C24
prime radicalC24×C17C23
hypercenterC2×#117D17
hypocenterC17C4×#117
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#117

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

Relationships

maximal subgroup of#16927765, #16927769, H(3,ℤ/4)×Dic17, …
maximal normal subgroup of#16927765, #16927769, H(3,ℤ/4)×Dic17, …
maximal quotient of#376×Dic17, C4×C22⋊C4×Dic17, C4×C4⋊C4×Dic17, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 6853);